TL;DR: In this article, a quasilinear Hopf-bifurcation analysis of the marginal stability boundary of a uniformly heated boiling channel is presented. But the analysis is restricted to the case when the effects of gravity and friction are considered.
Abstract: Thermally induced flow instabilities in uniformly heated boiling channels have been studied analytically. The classical homogeneous equilibrium model was used. This distributed model was transformed into an integrodifferential equation for inlet velocity. A linear analysis showed interesting features (i.e. islands of instability) of the marginal stability boundary which appear when the effects of gravity and friction were systematically considered. A quasilinear Hopf-bifurcation analysis, valid near the marginal-stability boundaries, gives the amplitude and frequency of limit-cycle oscillations that can appear on the unstable side of the boundary. The analysis also shows cases where a finite-amplitude perturbation can cause a divergent instability on the stable side of the linear-stability boundary.
TL;DR: The most popular models to predict the two-phase flow dynamic instabilities, namely the homogenous flow model and the drift-flux models are clarified with the solution examples and the validation of the model results with experimental findings are also provided.
Abstract: The earliest research in the field of two-phase flow was conducted by Lorentz (1909) The studies on the analysis of two-phase flow instabilities by Ledinegg (1938) created considerable interest concerning the phenomenon of thermally induced flow instability in two-phase flow systems The objective of this review is to sum up the experimental and theoretical work carried out by various investigators over a period of several years, demonstrating and explaining three main instability modes of two-phase flow dynamic instabilities, namely, density-wave type, pressure-drop type and thermal oscillations, encountered in various boiling flow channel systems The typical experimental investigations of these instabilities in tube boiling systems are indicated and the most popular models to predict the two-phase flow dynamic instabilities, namely the homogenous flow model and the drift-flux models are clarified with the solution examples and the validation of the model results with experimental findings are also provided
TL;DR: An updated review of two-phase flow instabilities including experimental and analytical results regarding density-wave and pressure-drop oscillations, as well as Ledinegg excursions, is presented in this article.
Abstract: An updated review of two-phase flow instabilities including experimental and analytical results regarding density-wave and pressure-drop oscillations, as well as Ledinegg excursions, is presented. The latest findings about the main mechanisms involved in the occurrence of these phenomena are introduced. This work complements previous reviews, putting all two-phase flow instabilities in the same context and updating the information including coherently the data accumulated in recent years. The review is concluded with a discussion of the current research state and recommendations for future works.
TL;DR: In this article, the drift flux model is used to make the set of equations dimensionless to ensure the mutual independence of the dimensionless variables and parameters: the steady-state inlet velocity v, the inlet subcooling number N sub and the phase change number N pch.
Abstract: Linear and nonlinear mathematical stability analyses of parallel channel density wave oscillations are reported. The two phase flow is represented by the drift flux model. A constant characteristic velocity v 0 ∗ is used to make the set of equations dimensionless to ensure the mutual independence of the dimensionless variables and parameters: the steady-state inlet velocity v , the inlet subcooling number N sub and the phase change number N pch . The exact equation for the total channel pressure drop is perturbed about the steady-state for the linear and nonlinear analyses. The surface defining the marginal stability boundary (MSB) is determined in the three-dimensional equilibrium-solution/operating-parameter space v − N sub − N pch . The effects of the void distribution parameter C 0 and the drift velocity V g j on the MSB are examined. The MSB is shown to be sensitive to the value of C 0 and comparison with experimental data shows that the drift flux model with C 0 > 1 predicts the experimental MSB and the neighboring region of stable oscillations (limit cycles) considerably better than do the homogeneous equilibrium model ( C 0 = 1, V g j = 0 ) or a slip flow model. The nonlinear analysis shows that supercritical Hopf bifurcation occurs for the regions of parameter space studied; hence stable oscillatory solutions exist in the linearly unstable region in the vicinity of the MSB. That is, the stable fixed point v becomes unstable and bifurcates to a stable limit cycle as the MSB is crossed by varying N sub and/or N pch .
TL;DR: In this paper, the state-of-the-art of flow instabilities in natural circulation boiling loops has been reviewed by reviewing a number of contributions made in the past three decades.
Abstract: Safety concerns of nuclear reactors have attracted the attention of researchers on flow instabilities in natural circulation boiling loops. This paper presents the state of the art in this area by reviewing a number of contributions. A large number of experimental and numerical investigations have been conducted to study and understand the conditions for inception of flow instabilities, parametric effects on instabilities, and the system behaviour under such conditions. Work done on instabilities due to channel thermal hydraulics as well as neutronics thermal hydraulics coupling has been reviewed. Different methods of analysis used by researchers and results obtained by them have been discussed. Various mathematical models and numerical techniques adopted for developing computer codes have also been discussed. The findings reported in the investigations made in the past three decades have been summarized to present the state of the art of the understanding of flow instabilities in natural circulation boiling systems.
TL;DR: A review of flow instabilities in boiling natural circulation systems has been carried out in this article, where an attempt has been made to classify the instabilities occurring in natural circulation system similar to that in forced convection boiling systems.
Abstract: Several decades have been spent on the study of flow instabilities in boiling two-phase natural circulation systems It is felt to have a review and summarize the state-of-the-art research carried out in this area, which would be quite useful to the design and safety of current and future light water reactors with natural circulation core cooling With that purpose, a review of flow instabilities in boiling natural circulation systems has been carried out An attempt has been made to classify the instabilities occurring in natural circulation systems similar to that in forced convection boiling systems The mechanism of instabilities occurring in two-phase natural circulation systems have been explained based on these classifications The characteristics of different instabilities as well as the effects of different operating and geometric parameters on them have been reviewed